Interpretable Machine Learning for Exchange Rate Forecasting with Macroeconomic Fundamentals

Table of Contents

1. Introduction

Forecasting exchange rates is notoriously difficult due to the complexity, nonlinearity, and frequent structural breaks in financial systems. Traditional econometric models often struggle to capture these dynamics and provide transparent explanations for their predictions. This study addresses this gap by developing a fundamental-based model for the Canadian–U.S. dollar (CAD/USD) exchange rate within an interpretable machine learning (IML) framework. The primary goal is not only to predict the exchange rate accurately but also to "open the black box" and explain the relationships between macroeconomic variables and the forecast, thereby increasing trust and actionable insights for economists and policymakers.

The research is motivated by Canada's status as a major commodity exporter, with crude oil constituting 14.1% of its total exports in 2019 and being the largest supplier to the U.S. This creates a hypothesized strong link between commodity prices (especially oil) and the CAD/USD rate, which the study aims to quantify and explain.

2. Methodology & Framework

2.1 Interpretable Machine Learning Approach

The core methodology involves using advanced machine learning models (e.g., Gradient Boosting Machines, Random Forests) capable of modeling complex, nonlinear relationships. To interpret these models, the study employs post-hoc interpretability techniques, notably SHAP (SHapley Additive exPlanations) values. SHAP values, rooted in cooperative game theory, quantify the contribution of each feature (macroeconomic variable) to a specific prediction, providing both global and local interpretability.

2.2 Model Architecture & Feature Selection

The model incorporates a wide range of macroeconomic fundamentals hypothesized to influence the CAD/USD rate. Key variables include:

• Commodity Prices: Crude oil price (WTI/Brent), gold price.
• Financial Indicators: S&P/TSX Composite Index (Canadian stock market), interest rate differentials (Canada vs. U.S.).
• Economic Fundamentals: GDP growth differentials, trade balance, inflation rates.

The study explicitly addresses the challenges of nonlinearity and multicollinearity among these variables, which are often overlooked in traditional univariate analyses.

3. Empirical Analysis & Results

3.1 Key Variable Importance

The interpretability analysis reveals a clear hierarchy of feature importance:

1. Crude Oil Price: The most significant determinant of CAD/USD dynamics. Its contribution is time-varying, changing in both sign and magnitude in response to major events in global energy markets and Canada's oil sector evolution.
2. Gold Price: The second most important variable, reflecting Canada's status as a major gold producer and gold's role as a safe-haven asset.
3. TSX Stock Index: The third key driver, representing broader investor sentiment and capital flows related to the Canadian economy.

3.2 Ablation Study for Model Improvement

An innovative aspect of this research is the use of an ablation study informed by interpretability outputs. After identifying the most important features via SHAP, the authors systematically retrain models by removing or adding features based on their interpreted contributions. This process refines the model, leading to improved predictive accuracy by focusing on the most relevant signals and reducing noise from less important or redundant variables.

3.3 Time-Varying Effects & Event Analysis

The SHAP analysis allows for the visualization of how feature contributions evolve over time. For instance, the impact of crude oil prices on the CAD/USD rate was found to intensify during periods of high oil price volatility (e.g., the 2014-2015 oil price crash, geopolitical tensions). This aligns with economic theory and provides empirical, model-backed evidence of structural breaks in the relationship.

4. Technical Implementation

4.1 Mathematical Formulation

The prediction model can be represented as: $\hat{y} = f(X)$, where $\hat{y}$ is the forecasted exchange rate return, $X$ is the vector of macroeconomic features, and $f(\cdot)$ is the complex ML model. SHAP values $\phi_i$ for each feature $i$ explain the deviation of the prediction $f(x)$ from the baseline expected value $E[f(X)]$:

$f(x) = E[f(X)] + \sum_{i=1}^{M} \phi_i$

Where $\sum_{i=1}^{M} \phi_i = f(x) - E[f(X)]$. The SHAP value $\phi_i$ is calculated as:

$\phi_i(f, x) = \sum_{S \subseteq M \setminus \{i\}} \frac{|S|! (M - |S| - 1)!}{M!} [f_x(S \cup \{i\}) - f_x(S)]$

This ensures a fair attribution of the prediction difference to each feature based on all possible combinations.

4.2 Analysis Framework Example

Scenario: Analyzing the CAD/USD forecast for Q4 2022.

Framework Steps:

1. Data Ingestion: Collect time-series data for all selected features (oil, gold, TSX, rates, etc.).
2. Model Prediction: Input the feature vector into the trained ML model to get forecast $\hat{y}$.
3. SHAP Explanation: Compute SHAP values for this prediction instance.
4. Interpretation: The output shows: Oil: +0.015 (strong positive contribution), Gold: -0.005 (mild negative), TSX: +0.002 (positive). This indicates the model's prediction of a stronger CAD is primarily driven by high oil prices, slightly offset by lower gold prices.
5. Ablation Check: A model retrained without gold might show minimal accuracy loss, confirming its secondary role, while removing oil would severely degrade performance.

5. Discussion & Implications

5.1 Core Insights for Policymakers

The study provides actionable intelligence: Monetary and fiscal policy in Canada must be acutely aware of crude oil price dynamics. Efforts to diversify the export base could reduce exchange rate volatility. The model itself can serve as a monitoring tool, where sharp changes in SHAP values for key commodities signal potential upcoming FX pressure.

5.2 Strengths & Limitations

Strengths: Successfully integrates high predictive power with explainability; validates economic intuition with data-driven evidence; introduces a useful feedback loop via interpretation-driven ablation.

Limitations: Interpretability methods like SHAP are approximations; the model's performance is contingent on the quality and relevance of the chosen fundamentals; may not fully capture "black swan" events or sudden regime changes not present in historical data.

6. Future Applications & Directions

The framework is highly generalizable:

• Other Currency Pairs: Applying the same IML approach to commodity-driven currencies like AUD, NOK, or RUB.
• Real-Time Policy Dashboard: Developing a dashboard that visualizes SHAP values in real-time for central bank analysts.
• Integration with Alternative Data: Incorporating news sentiment, shipping data, or satellite imagery of oil infrastructure to enhance forecasts.
• Causal Discovery: Using interpretability outputs as a starting point for more formal causal inference analysis to move beyond correlation.
• Explainable AI (XAI) Standards: Contributing to the development of best practices for using IML in sensitive economic policymaking, akin to standards discussed in research from institutions like the Bank for International Settlements (BIS).

7. References

1. Lundberg, S. M., & Lee, S. I. (2017). A Unified Approach to Interpreting Model Predictions. Advances in Neural Information Processing Systems 30 (NIPS 2017).
2. Molnar, C. (2022). Interpretable Machine Learning: A Guide for Making Black Box Models Explainable. (2nd ed.).
3. Bank for International Settlements (BIS). (2020). The rise of AI in finance: a survey. BIS Papers.
4. Chen, S. S., & Chen, H. C. (2007). Oil prices and real exchange rates. Energy Economics, 29(3), 390-404.
5. Ferraro, D., Rogoff, K., & Rossi, B. (2015). Can oil prices forecast exchange rates? An empirical analysis of the relationship between commodity prices and exchange rates. Journal of International Money and Finance, 54, 116-141.

8. Original Analysis & Expert Commentary